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ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
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that the research results should be composed of not only a set of 
decision alternatives (presented as research reports) but also a 
computer management system (presented as computer software 
packages). Decision-makers can then keep inputting varied 
information (for the future periods) to the software and obtaining 
updated solutions. Thus, new alternatives can be obtained 
through interpretation of the solutions. 
Multi-objective Feature 
In the study system under consideration, there exist many 
environmental, socio-economic, and resources objectives, which 
are of concern to a number of stakeholders bearing different 
interests. These objectives also interact to each other, with 
potentials of limiting or promoting each other. Thus, the problem 
under consideration is how to make tradeoff or compromise 
between interests from different stakeholders, in order to 
maximize overall benefits of the entire system. 
Uncertain Feature 
Many system components and their interrelationships are 
uncertain in the study system. Normally, people get used of 
using mean value or middle value to represent uncertain 
information. However, for a system with many uncertain factors, 
this approximation may lead to loss of information. For example, 
it is hard to obtain deterministic value of loading capacity for 
tourists at a sightseeing spot. Instead, only some uncertain 
information is available. If we simply present it by a mean or 
middle value, reliability of the resulting planning may be affected. 
The above descriptions demonstrate complexity of the study 
system. Thus, simple decision or expert consultation would not 
be good enough for generating an effective decision support. 
Employment of systems analysis methods that can incorporate a 
variety of system components within a general modeling 
framework is desired. 
WATERSHED MODELING 
A watershed is a complex system with human activities in water 
and in land. It is impossible to use a single model to reflect a 
variety of activities in a watershed. This study developed a 
modeling system containing three major components: (i) 
simulation models which are useful for bridging source/impact 
factors and the related water quality, as well as predicting 
system behaviors under different conditions; (ii) optimization 
models which will be used for compromising a variety of system 
objectives and generating desired decision alternatives; and (iii) 
post-simulation/optimization models for further trade-off analysis 
and risk assessment in order to facilitate practical 
implementation of the generated alternatives applied to analyze. 
Simulation Modeling 
The mechanisms of pollutant transport in a watershed are very 
complex, involving many factors such as hydrological, 
topographical, chemical and biological processes, as well as soil- 
type and land use conditions. These factors are related to both 
point and non-point source pollution problems. For effective 
watershed management and planning, an important issue is the 
ability to simulate and predict impacts of human activities and 
related environmental conditions on both water quantity and 
quality. In this study, hydrologic/water quality (H/WQ) models 
have been developed to link a number of human activities to 
their pollution impacts. Four major processes, including 
hydrological cycle, soil erosion, and water quality, are simulated. 
QUAL2E is widely used for modeling water quality of well mixed 
and dendritic streams (Brown et al., 1987). It simulates the major 
reactions of nutrient cycles, algal production, benthic and 
carbonaceous demand, atmospheric reaeration, and their effects 
on the dissolved oxygen balance. It can be used for predicting 
concentrations of up to 15 water quality constituents. 
For the hydrological cycle, HSPF (Bicknell et al., 1997) simulates 
for extended periods of time the hydrologic processes, and 
associated water quality, on pervious and impervious land 
surfaces and in streams and well-mixed impoundments. HSPF is 
generally used for assessing the effects of land-use change, 
reservoir operations, point or non-point source pollution control, 
and flow diversions, etc. 
The USLE (Universal Soil Loss Equation) (Renard et al., 1991) 
estimates annual sheet and rill erosion as affected by six factors: 
rainfall erovisity, soil erodibility, slope length, slope steepness, 
cover and management, and conservation practices. Concepts 
of USLE have been customized to the detailed study basin, 
which provides prediction of soil loss under different hydrological, 
climatological and landscape conditions (Huang, 1995a). Since 
the majority of parameters related to soil loss are uncertain in 
their nature, probabilistic and inexact analyses for the 
uncertainties will be undertaken throughout the modeling 
process. 
Optimization Modeling 
An inexact-fuzzy multiobjective linear programming (IFMOP) 
model is developed to form an environmental decision support 
system, in association with a number of simulation/evaluation 
tools. The IFMOP is proposed by extending the inexact fuzzy 
linear programming (IFLP) method (Huang et al., 1993) to a 
multiobjective decision-making problem. An interactive approach 
is proposed for conveniently obtaining indispensable intervention 
from decision-makers during the IFMOP modeling process. 
The IFLP was developed as a branch of inexact mathematical 
programming (Huang, 1994) which is effective for optimization 
under incomplete uncertainty (e.g. information with known 
fluctuation intervals but unknown probabilistic or possibilistic 
distributions). The method has been successfully applied to a 
variety of management and planning problems (Huang, 1994, 
Huang, 1996; Huang et al., 1996; Yeh, 1995). The IFMOP is a 
hybrid of the IFLP and fuzzy multiobjective program 
Membership functions for both objectives and constraints are 
formulated to reflect uncertainties in different system 
components and their interrelationships. A solution algorithm for 
inexact linear programming (Huang, 1996) is employed to handle 
uncertainties in the lefthand side coefficients. Thus, the IFMOP 
allows uncertainties to be directly communicated into the 
programming processes and resulting solutions. Its inexact 
solutions can be interpreted for generating decision alternatives 
and conducting further risk analyses. Also, the IFMOP solution 
approaches do not lead to complicated intermediate submodels, 
and thus have reasonable computational requirements. A 
general multiobjective linear programming problem with inexact 
parameters can be formulated as follows: 
min 
fk* = (Vx*, 
k = 1,2 p, 
(1a) 
max 
f* = ctx\ 
/= p+1, p+2, ... 
,q, (1b) 
s.t. 
Aj'X* < b*, 
i = 1, 2, ... , m, 
(1C) 
A^X* > bj*. 
j = m+1, m+2,.. 
. ,n, (id) 
X*>0, 
(1e) 
where 
X± e {«±}tx1, 
Ck± e{1R±}1xt, Cl± 
e{in±}1xt, Ai± e 
{iR±}1xt, Aj± e {ït±}1 xt, and s Jt± denotes a set of interval 
numbers. 
When all parameters in model (1) are known as intervals without 
distribution information, this is an inexact multiobjective 
programming (IMOP) problem. When some of the parameters 
are assigned with membership functions, the model becomes a 
hybrid inexact-fuzzy MOP (IFMOP) problem. In this study, the